This puzzle is not trivial. I wanted to have a sequence (macro) which flipp=
s to neighbouring edges. A little by luck I found such a sequence which got=
the name a13. Doing a walk which brings back an edge in flipped state take=
s a lot of place and it is not easy to find a 3-cycle in the complement. Ap=
plying this macro is not easy in this puzzle. Having the reference point in=
between the two flipped edges I had to try all 5 positions in the face to f=
ind the only one which works (in wrong positions there was no effect or com=
pletely other effects than a double flip). With a setup it was always possi=
ble to get arround this problem.
I think the problem is typical for the topology of this puzzle. Can anybody=
of you do a more profound analysis? Is this puzzle 1-sided? Is it orientab=
le? We have only 8 colors what forces a non trivial "glueing" of edges (ori=
ented edges?).
I uplaod my macrofile for this puzzle on the 4D cubing group. Try the macro=
a13.
--------------090201070600060604020709
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit
Hello Eduard,
I tried your macro a13
and it is interesting. I've not used the macros in TM before so I'm not
sure how they are supposed to be used but when I click on a red face
near the vertex adjacent to the white and blue face it indeed exchanges
two edges but click it elsewhere makes a mess. This was done in the
hyperbolic view (Show as Skew = false) because in IRP mode I get an
error saying that macros are not available in IRP mode. It does seem to
work anyway, so maybe it is fine for this model though I'm not certain
that the behavior is the same as in the hyperbolic view. Regardless,
this is certainly an excellent macro and probably all one would need to
solve this odd, unlikely and lovely little puzzle.
Strange as it may be, I am fairly certain that it is still an orientable
surface. It has genus 3 which is common. I don't know if there is
anything odd about its topology and would be interested to learn
anything more about it that people may discover.
-Melinda
On 4/24/2012 4:51 AM, Eduard wrote:
> This puzzle is not trivial. I wanted to have a sequence (macro) which flipps to neighbouring edges. A little by luck I found such a sequence which got the name a13. Doing a walk which brings back an edge in flipped state takes a lot of place and it is not easy to find a 3-cycle in the complement. Applying this macro is not easy in this puzzle. Having the reference point inbetween the two flipped edges I had to try all 5 positions in the face to find the only one which works (in wrong positions there was no effect or completely other effects than a double flip). With a setup it was always possible to get arround this problem.
> I think the problem is typical for the topology of this puzzle. Can anybody of you do a more profound analysis? Is this puzzle 1-sided? Is it orientable? We have only 8 colors what forces a non trivial "glueing" of edges (oriented edges?).
> I uplaod my macrofile for this puzzle on the 4D cubing group. Try the macro a13.\
--------------090201070600060604020709
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
http-equiv="Content-Type">
Hello Eduard,
I tried your
a13 and it is interesting. I've not used the macros in TM
before so I'm not sure how they are supposed to be used but when I
click on a red face near the vertex adjacent to the white and blue
face it indeed exchanges two edges but click it elsewhere makes a
mess. This was done in the hyperbolic view (Show as Skew = false)
because in IRP mode I get an error saying that macros are not
available in IRP mode. It does seem to work anyway, so maybe it is
fine for this model though I'm not certain that the behavior is the
same as in the hyperbolic view. Regardless, this is certainly an
excellent macro and probably all one would need to solve this odd,
unlikely and lovely little puzzle.
Strange as it may be, I am fairly certain that it is still an
orientable surface. It has genus 3 which is common. I don't know if
there is anything odd about its topology and would be interested to
learn anything more about it that people may discover.
-Melinda
On 4/24/2012 4:51 AM, Eduard wrote:
This puzzle is not trivial. I wanted to have a sequence (macro) which flipps to neighbouring edges. A little by luck I found such a sequence which got the name a13. Doing a walk which brings back an edge in flipped state takes a lot of place and it is not easy to find a 3-cycle in the complement. Applying this macro is not easy in this puzzle. Having the reference point inbetween the two flipped edges I had to try all 5 positions in the face to find the only one which works (in wrong positions there was no effect or completely other effects than a double flip). With a setup it was always possible to get arround this problem.
I think the problem is typical for the topology of this puzzle. Can anybody of you do a more profound analysis? Is this puzzle 1-sided? Is it orientable? We have only 8 colors what forces a non trivial "glueing" of edges (oriented edges?).
I uplaod my macrofile for this puzzle on the 4D cubing group. Try the macro a13.\
--------------090201070600060604020709--
Hi,
I just tried this puzzle. I agree that it's not trivial at all. I've probab=
ly tried this puzzle a long time ago but I found it too asymmetric, so I ga=
ve up. But today I solved it.=20
Around each vertex, "two" faces out of the "five" are identified, which bre=
aks the symmetry. So the five "angles" around a vertex are not equivalent. =
For the same reason, the reference point can only be in a certain type of a=
ngle. The fact that different reference points lead to different results is=
not a bug. It's just a consequence of asymmetry: if you hold the puzzle di=
fferently and apply the same sequence, the result is different.
As I understand it, to flip an edge, the main idea is nothing but to let it=
go around a vertex. It's a bit tricky not to affect other pieces. When I s=
olved it I tried to apply [1,1] commutators intuitively and watched the ori=
entation carefully at the same time. So I didn't use macro for flipping edg=
es. But I recorded a sequence which flips two edges in place, just to expla=
in what I would do. It can be found here:
http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/IRP55_flip.xml
It's just a save file, not a macro. You can use ctrl+z to go back to the st=
arting point and use ctrl+y to play it. There are 14 moves. The first 8 mov=
es are the first 3-cycle: 2 setup moves + [1,1] commutator + undo setup mov=
es. The next 6 moves are the second 3-cycle: 1 setup move + [1,1] commutato=
r + undo setup move. The idea is just to take an edge and let it go around =
a vertex.=20
It's funny that the eight colors form four pairs: cyan+blue, green+orange, =
white+yellow, red+purple. The two colors in each pair have a special geomet=
ric relation, so that they intersect by two pieces. So their commutator is =
not a 3-cycle. To construct a 3-cycle using commutators, one should avoid u=
sing such pairs. Two colors from different pairs (for example red and white=
) intersect by one piece so their commutator is a 3-cycle.=20
It seems like the paired pentagons have more stories in terms of geometry/t=
opology. In the IRP view, they are co-planar. I'm not good at topology but =
I'd love it if any one explain it.
****
By the way, a completely independent thing: here's the wallpaper I've been =
using for a while.=20
http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/Image 000.png=
=20
It was generated by Magic Tile v2 by choosing a particular puzzle with prop=
er parameters. No photoshop involved. Does anyone know what puzzle is it?
Nan
--- In 4D_Cubing@yahoogroups.com, Melinda Green
>
> Hello Eduard,
>=20
> I tried your macro a13=20
>
%7D%208c%20F%200-0-0%2C85%20macros.xml>=20
> and it is interesting. I've not used the macros in TM before so I'm not=20
> sure how they are supposed to be used but when I click on a red face=20
> near the vertex adjacent to the white and blue face it indeed exchanges=20
> two edges but click it elsewhere makes a mess. This was done in the=20
> hyperbolic view (Show as Skew =3D false) because in IRP mode I get an=20
> error saying that macros are not available in IRP mode. It does seem to=20
> work anyway, so maybe it is fine for this model though I'm not certain=20
> that the behavior is the same as in the hyperbolic view. Regardless,=20
> this is certainly an excellent macro and probably all one would need to=20
> solve this odd, unlikely and lovely little puzzle.
>=20
> Strange as it may be, I am fairly certain that it is still an orientable=
=20
> surface. It has genus 3 which is common. I don't know if there is=20
> anything odd about its topology and would be interested to learn=20
> anything more about it that people may discover.
>=20
> -Melinda
>=20
> On 4/24/2012 4:51 AM, Eduard wrote:
> > This puzzle is not trivial. I wanted to have a sequence (macro) which f=
lipps to neighbouring edges. A little by luck I found such a sequence which=
got the name a13. Doing a walk which brings back an edge in flipped state =
takes a lot of place and it is not easy to find a 3-cycle in the complement=
. Applying this macro is not easy in this puzzle. Having the reference poin=
t inbetween the two flipped edges I had to try all 5 positions in the face =
to find the only one which works (in wrong positions there was no effect or=
completely other effects than a double flip). With a setup it was always p=
ossible to get arround this problem.
> > I think the problem is typical for the topology of this puzzle. Can any=
body of you do a more profound analysis? Is this puzzle 1-sided? Is it orie=
ntable? We have only 8 colors what forces a non trivial "glueing" of edges =
(oriented edges?).
> > I uplaod my macrofile for this puzzle on the 4D cubing group. Try the m=
acro a13.\
>
Edit: the URL of the image should be:
http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/Image%20000.pn=
g
Some email interface doesn't interpret the space as part of the URL. Sorry.
--- In 4D_Cubing@yahoogroups.com, "schuma"
>
> Hi,
>=20
> I just tried this puzzle. I agree that it's not trivial at all. I've prob=
ably tried this puzzle a long time ago but I found it too asymmetric, so I =
gave up. But today I solved it.=20
>=20
> Around each vertex, "two" faces out of the "five" are identified, which b=
reaks the symmetry. So the five "angles" around a vertex are not equivalent=
. For the same reason, the reference point can only be in a certain type of=
angle. The fact that different reference points lead to different results =
is not a bug. It's just a consequence of asymmetry: if you hold the puzzle =
differently and apply the same sequence, the result is different.
>=20
> As I understand it, to flip an edge, the main idea is nothing but to let =
it go around a vertex. It's a bit tricky not to affect other pieces. When I=
solved it I tried to apply [1,1] commutators intuitively and watched the o=
rientation carefully at the same time. So I didn't use macro for flipping e=
dges. But I recorded a sequence which flips two edges in place, just to exp=
lain what I would do. It can be found here:
>=20
> http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/IRP55_flip.x=
ml
>=20
> It's just a save file, not a macro. You can use ctrl+z to go back to the =
starting point and use ctrl+y to play it. There are 14 moves. The first 8 m=
oves are the first 3-cycle: 2 setup moves + [1,1] commutator + undo setup m=
oves. The next 6 moves are the second 3-cycle: 1 setup move + [1,1] commuta=
tor + undo setup move. The idea is just to take an edge and let it go aroun=
d a vertex.=20
>=20
> It's funny that the eight colors form four pairs: cyan+blue, green+orange=
, white+yellow, red+purple. The two colors in each pair have a special geom=
etric relation, so that they intersect by two pieces. So their commutator i=
s not a 3-cycle. To construct a 3-cycle using commutators, one should avoid=
using such pairs. Two colors from different pairs (for example red and whi=
te) intersect by one piece so their commutator is a 3-cycle.=20
>=20
> It seems like the paired pentagons have more stories in terms of geometry=
/topology. In the IRP view, they are co-planar. I'm not good at topology bu=
t I'd love it if any one explain it.
>=20
> ****
>=20
> By the way, a completely independent thing: here's the wallpaper I've bee=
n using for a while.=20
>=20
> http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/Image 000.pn=
g=20
>=20
> It was generated by Magic Tile v2 by choosing a particular puzzle with pr=
oper parameters. No photoshop involved. Does anyone know what puzzle is it?
>=20
> Nan
>=20
>=20
>=20
> --- In 4D_Cubing@yahoogroups.com, Melinda Green
> >
> > Hello Eduard,
> >=20
> > I tried your macro a13=20
> >
C5%7D%208c%20F%200-0-0%2C85%20macros.xml>=20
> > and it is interesting. I've not used the macros in TM before so I'm not=
=20
> > sure how they are supposed to be used but when I click on a red face=20
> > near the vertex adjacent to the white and blue face it indeed exchanges=
=20
> > two edges but click it elsewhere makes a mess. This was done in the=20
> > hyperbolic view (Show as Skew =3D false) because in IRP mode I get an=20
> > error saying that macros are not available in IRP mode. It does seem to=
=20
> > work anyway, so maybe it is fine for this model though I'm not certain=
=20
> > that the behavior is the same as in the hyperbolic view. Regardless,=20
> > this is certainly an excellent macro and probably all one would need to=
=20
> > solve this odd, unlikely and lovely little puzzle.
> >=20
> > Strange as it may be, I am fairly certain that it is still an orientabl=
e=20
> > surface. It has genus 3 which is common. I don't know if there is=20
> > anything odd about its topology and would be interested to learn=20
> > anything more about it that people may discover.
> >=20
> > -Melinda
> >=20
> > On 4/24/2012 4:51 AM, Eduard wrote:
> > > This puzzle is not trivial. I wanted to have a sequence (macro) which=
flipps to neighbouring edges. A little by luck I found such a sequence whi=
ch got the name a13. Doing a walk which brings back an edge in flipped stat=
e takes a lot of place and it is not easy to find a 3-cycle in the compleme=
nt. Applying this macro is not easy in this puzzle. Having the reference po=
int inbetween the two flipped edges I had to try all 5 positions in the fac=
e to find the only one which works (in wrong positions there was no effect =
or completely other effects than a double flip). With a setup it was always=
possible to get arround this problem.
> > > I think the problem is typical for the topology of this puzzle. Can a=
nybody of you do a more profound analysis? Is this puzzle 1-sided? Is it or=
ientable? We have only 8 colors what forces a non trivial "glueing" of edge=
s (oriented edges?).
> > > I uplaod my macrofile for this puzzle on the 4D cubing group. Try the=
macro a13.\
> >
>